Renewable and Sustainable Energy Reviews (xxxx) xxxx–xxxx

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Renewable and Sustainable Energy Reviews

journal homepage: www.elsevier.com/locate/rser

A review of nonimaging solar concentrators for stationary and passive tracking applications ⁎ Srikanth Madala , Robert F. Boehm

Center for Energy Research, Department of Mechanical Engineering, University of Nevada, Las Vegas 89154-4027, United States

ARTICLE INFO ABSTRACT

Keywords: The solar energy research community has realized the redundancy of image-forming while collecting/ Solar concentrators concentrating solar energy with the discovery of the nonimaging type radiation collection mechanism in Nonimaging 1965. Since then, various nonimaging concentration mechanisms have proven their superior collection CPC efficiency over their imaging counter-parts. The feasibility of using nonimaging concentrators successfully for Compound parabolic concentrator stationary applications has rekindled interest in them. The economic benefits are appealing owing to the V-trough elimination of tracking costs (installation, operation & maintenance and auxiliary energy). This paper is an Polygonal trough Concentration ratio exhaustive review of the available nonimaging concentrating mechanisms with stationary applications in mind. Non-tracking solar concentrators This paper also explores the idea of coupling nonimaging concentrators with passive solar tracking mechanism. Stationary solar concentrators CHC CEC Compound hyperbolic concentrators Compound elliptical concentrators Nonimaging Fresnel Dielectric compound parabolic concentrators DCPC Trumpet-shaped concentrators

1. Introduction traditional imaging techniques of concentration fall short of the thermodynamic limit of maximum attainable concentration at least Amongst the total solar electric power worldwide today (as per by a factor of four due to severe off-axis aberration and coma causing 2015 data) [1], solar photovoltaics (PV) contribute about 227 GW, and image blurring and broadening. Imaging is an inhibitive phenomenon concentrating solar power (CSP) technologies contribute about 4.8 GW as far as only energy concentration is concerned. The concentration of in generation capacity. NREL's SolarPACES program constantly moni- solar energy does not demand imaging qualities, but instead requires tors and updates the global list of CSP projects that are either flexible concentrator designs coping with solar disk size, solar spec- operational or currently under development [2]. The trum, and tracking errors while delivering a highly uniform flux [4]. (an imaging-type solar concentrator technology) accounts for a vast Moreover, an active solar tracking mechanism, often accompanying an majority of the CSP installations worldwide due to its cost advantage, imaging concentrator, also adds to the capital and O & M costs while although power tower systems are quickly catching up. United States consuming a fraction of the power produced. Therefore, with all these and Spain being the front-runners, various other nations including the disadvantages in view, nonimaging and stationary techniques of Middle East and North Africa (MENA) countries, South Africa, India, concentrating solar radiation are sought after. and China are fast adopting CSP [3]. Nonimaging concentrators have been used in solar energy collec- No matter the type of CSP technology adopted, actively tracking the tion systems ever since their discovery in 1965. In the decades that Sun in order to achieve meaningful concentration is a common trait in followed, various nonimaging concentrator designs were discovered all of them. The concentration of solar radiation is typically achieved by and evaluated as stationary installations. The concentration ratios using an active solar tracking mechanism coupled with a point- or line- achieved were typical low ( < 3X) or medium (3-10X). However, the focus imaging concentration system. However, even the best of the application of these types of concentrators on a large scale or a utility

⁎ Corresponding author. E-mail address: [email protected] (S. Madala). http://dx.doi.org/10.1016/j.rser.2016.12.058 Received 6 February 2016; Received in revised form 14 November 2016; Accepted 8 December 2016 1364-0321/ © 2016 Elsevier Ltd. All rights reserved.

Please cite this article as: Madala, S., Renewable and Sustainable Energy Reviews (2016), http://dx.doi.org/10.1016/j.rser.2016.12.058 S. Madala, R.F. Boehm Renewable and Sustainable Energy Reviews (xxxx) xxxx–xxxx

Nomenclature hcd Conductive Heat Transfer Coefficient hR Radiative Heat Transfer Coefficient CPC Compound Parabolic Concentrator htot Overall Heat Transfer Coefficient ACPC Asymmetric Compound Parabolic Concentrator Htrunc Height of the truncated CPC BIPV Building Integrated Photovoltaics LVT -V Trough CCAC Compound Circular Arc Concentrator MENA Middle East and North Africa CEC Compound Elliptical Concentrator n of the Dielectric Media CHC Compound Hyperbolic Concentrator NREL National Renewable Energy Laboratory CPV Concentrated Photovoltaics O&M Operation and Maintenance CR Concentration Ratio PCCPC Prism-coupled Compound Parabolic Concentrator CSP PV Photovoltaics CSP Concentrated Solar Power RReflector-To-Aperture Ratio

d1 Dimension of Entrance Aperture SPC Simple Parabolic Concentrator d2 Dimension of Exit Aperture α Absorptivity DACPC Dielectric Asymmetric Parabolic Concentrator β Prism Apex Angle DCPC Dielectric Compound Parabolic Concentrator δ Complete Acceptance Angle of V-trough ER Energy Ratio ε Emissivity F(θ) Angular Acceptance Function θ Angle of Incidence of an Arbitrary

FDTD Finite-Difference Time-Domain θaor θmax Acceptance Angle GW Giga Watt θd Truncated CPC's Edge Ray Angle H Height of the CPC Φ Half Angle Of The V-Shaped Cone

hc Convective Heat Transfer Coefficient scale is yet to be materialized. This current paper is a review of the form an image of the light source. Unlike the conventional imaging presently existing and upcoming nonimaging techniques for concen- concentration systems, the quality of the image at the exit aperture is of tration of solar radiation in stationary or passive tracking applications. least importance in these concentrators. An illustration of a hypothe- Novel applications, and modern techniques of raytracing analysis on tical nonimaging concentration system is shown in Fig. 1. The concept nonimaging concentrators has also been discussed as a part of this of nonimaging collection of radiation came into the picture when the review. compound parabolic concentrator (CPC) was proposed by Hinterberg and Winston in 1965 as an efficient means of measuring Čerenkov 2. Stationary solar energy collectors radiation. The early 70 s saw a tremendous rise in the number of researchers experimenting on application of various CPC/modified Stationary solar energy collector designs such as a flat plate and a CPC designs as solar concentrators. All these nonimaging collector concentric cylindrical tube have been prevalent in low temperature ( < designs obey a fundamental principle known as the edge-ray principle 200° F) applications such as solar domestic/pool water heating, (used in the design of nonimaging optics) which can be summed up as: “ dehydration of agricultural products, etc. since the beginning of the if the edge or boundary rays from a source to an optical system fl 20th century [5]. As early as the mid-1970s, Falbel Energy System (re ective or refractive) are able to be directed to the edges of a target Corp. manufactured a stationary ‘nonimaging’ collector (called the FES area, then all the rays in between these edge rays will also be directed to ” delta solar collector) with a cylindrical cavity trough that achieved a net the target area . Winston et al. [8] demonstrated the edge-ray principle fi gain of 2.3X compared to a flat plate collector. Another company using the string method. The same principle has also been re ned by named Kaptron manufactured a modified stationary flat-plate solar using a topological approach [9]. collector by incorporating a window with optical ribs, an optical valve The properties of various nonimaging CPC-type concentrators and a multi-reflection absorber enclosed in an insulated casing, thus including the compound elliptical concentrator (CEC), compound making it more efficient over a conventional design [6]. In more recent hyperbolic concentrator (CHC), trumpet-shaped concentrator and fl times, a Stationary V-trough collector (cone angle=60°) was fabricated generalized involute re ectors were discussed by Gordon and Rabl fl and tested in a solar water heating application for the geographical [10]. A comparative review on various re ective type solar concen- location of Kuala Lumpur (3.2°N and 101° 44′ E) [7]. The collector was trators has been reported as well [11]. Collector characteristics such as oriented in the E-W direction with 0° tilt angle. With a surface area of geometric concentration ratio, acceptance angle, sensitivity to 0.56 m2, it achieved a diurnal power collection that varied between 0.154 and 0.261 kW. When compared with respect to a flat-plate absorber, the average relative solar concentration ratios of the V-trough varied between 1.19 and 1.85 throughout the year. Interestingly, the peak summer and winter months saw a decrement in the relative concentration ratio.

3. Nonimaging solar concentrators

Nonimaging concentrators are a classification of radiation collec- tors that direct the radiative energy passing the entry aperture (larger area, A1) of the concentration system through to the exit aperture (smaller area, A2) with minimum optical losses. The term ‘nonimaging’ or ‘anidolic’ (from Greek an: without, eidolon: image) refers to the ‘ ’ virtue of the concentration system to focus the étendue or throughput Fig. 1. Illustration of a nonimaging concentration system with entry flux (Φ1) and exit on a wider area rather than a single focal point and, thus, unable to flux (Φ2).

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Fig. 2. A compound parabolic concentrator.

upcoming designs of nonimaging concentrators in greater detail with stationary or passive tracking application in perspective.

3.1. Compound parabolic concentrator

The basic design of a CPC concentrator is as shown in Fig. 2.AD and BC are two different parabolic profiles with foci at the end points of the exit aperture – B and A respectively. The tangential lines with respect to BC and AD at the end points of exit aperture – B and A – form the axes of the parabolas AD and BC respectively. A ray-tracing analysis of a hollow CPC (often referred to as a 2D CPC as it focuses on to a 2D plane) is shown in Fig. 3. The CPC attracted immediate attention of the solar energy research community with a capability of concentrating solar radiation by a factor of ~10 with just seasonal adjustment and minimal diurnal tracking [15]. For a stationary CPC, a concentration factor of ~3 is quite plausible. Also, the efficiency of accepting diffuse solar radiation enhanced further interest in their study.

3.1.1. Comparison of CPCs with other solar collectors The comparison between a simple parabolic concentrator (SPC) and a compound parabolic concentrator (CPC) has been made to show how the geometric concentration ratio of the SPC is lower by at least a factor Fig. 3. TracePro illustration of the working principle of hollow CPC concentrator. of π compared to the CPC with same acceptance angle [16]. A simple calculation shows that for a case of concentration ratio, CR=10, a CPC errors, reflector area, and average number of reflections were com- uses 4.4 times the amount of material used by a SPC. However, CPC pared. The family of compound parabolic concentrators (CPCs) with also has 3.15 times more acceptance angle for the same case. various reflector and absorber geometries, Fresnel , V-trough A typical limiting value of concentration ratios of CPCs and SPCs in concentrators and conventional imaging type concentrator designs order to enable collection of circumsolar radiation was calculated to be such as parabolic trough were discussed in this review. Furthermore, 19.1 and 6.1 respectively which corresponds to an acceptance angle of two-stage concentration systems with Fresnel mirrors as a primary 3° [16]. The reason for this limit being that the typical additional stage and CPC or V-trough as a secondary stage were also discussed. amount of circumsolar radiation available at smaller acceptance angles More recently, O’Gallagher [12] described various nonimaging collec- of 1°, 2° and 3° are 13%, 20% and 22% more than that compared to the −3 tor designs in his retrospection of the research work carried out at the intensity of the solar disk alone (solar disk ~4.65×10 rad or 0.266°). University of Chicago during the past 30 years. A review on solar Beyond a 3° acceptance angle, the effect of circumsolar radiation is photovoltaic concentrators briefly discussed a few designs of nonima- negligible. 2 ging concentrators such as CPC, CHC, quantum dot concentrator, A large-area (13.6 m ) of stationary CPC collector (with flat dielectric total internally reflecting concentrator (DTIRC), and multi- absorbers) was compared against a stationary flat plate collector, both stage concentrators [13]. Another similar review also presented a few collectors oriented in E-W direction [17]. The CPC recorded a thermal more nonimaging concentrator designs for concentrated photovoltaic loss coefficient that is 0.8 W/m2/K lower than the flat-plate collector application [14]. The convex-shaped nonimaging , and owing to the absorption of solar radiation by the reflectors and thus various other innovative multistage collector designs were discussed. smaller losses to the cover from the absorber surface. Usage of low The following sub-sections describe a few prominent existing and emissive reflectors and Teflon film as a transparent insulation between the cover and the absorber were the measures to improve the

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performance. The optical efficiency of the considered CPC (θa=35°, CR=1.53) was about 0.75 compared to 0.80 of its flat-plate counter- part. The difference in optical performance was too minor to compare given the fact that different types of material were used in the two collectors.

3.1.2. Experimentation with CPC absorber designs Various types of absorbers (viz. flat plate, cylindrical etc.) are used depending on the application of the CPC collector. Some of the commonly used absorber cross-sectional geometries are shown in Fig. 4, where Fig. 4A, Fig. 4B, Fig. 4C and Fig. 4D show flat, cylindrical, vertical fin, and wedge-shaped absorber geometries that are more common while Fig. 4E shows a non-typical dual-cavity absorber that is used with a CPC [18]. The dual-cavity absorber (enlarged geometry as shown in Fig. 4E) was tested against a cylindrical absorber of similar dimensions on a CPC under same test conditions [19]. An improvement in the optical efficiency by about 15–17% is reported for paraxial irradiance. This type of absorber design may be useful when coupled with an active tracking CPC. Some other commonly used absorber designs such as the bottom tube sheet and the top embossed honeycomb surface (as shown in Fig. 5) have been discussed [6]. An embossed honeycomb design showed an improvement in solar absorption by about 3.7–22.9% for radiation at angles varying from 15° to 70°. Toughened aluminum is a good material choice for these absorber surfaces. The absorptivity (α) to emissivity (ε) ratio is increased by using a thin coating of special black nickel. Winston et al. [20] described the fabrication, testing and applica- tion of the integrated compound parabolic concentrator (ICPC) which integrates a CPC into an evacuated glass tube collector thereby eliminating the need for additional mechanical structure. An array of 336 ICPC collectors (100 m2 area) are used to drive a 20-ton double effect absorption type chiller.

3.1.3. Thermal performance of CPCs A detailed thermal analysis describing the radiative, convective and conductive heat transfer in CPCs along with interplay between them was carried out by Rabl [21]. The convective heat loss is predominant in CPCs with selective absorber coating while radiative heat loss tends to dominate in CPCs with non-selective absorber coating. Using either selective coating or microcavity surface structure for the absorber will increase the absorption, however using both is counter-productive. The paper also warns against heat loss through a potential cooling fineffect created by conductive reflector material (especially when using alumi- num sheet). The thermal performance of the CPC with a flat one-sided absorber has been theoretically analyzed where in the effect of various design parameters (fluid flow rate, inlet temperature, CPC length, selective absorber coating, mirror reflectance etc.) were discussed [22]. The daily efficiency of the collector increased with the fluid flow rate, whereas it decreased with the increase in the inlet temperature and the trough length of the CPC. The selective absorber coating and mirror reflectance are more effective in cases when the solar radiation collection peaks (around solar noon time).

3.1.4. Truncation of CPCs The major disadvantage of a CPC is the larger depth at higher concentrations. For instance, a CPC with concentration ratio of 10 has areflector-to-aperture area ratio of 11. While this number in case of a simple parabolic concentrator is around 1.1–1.2 [21]. Hence, the CPCs Fig. 4. Various absorber geometries used in CPCs [18,19]. are often truncated (from the aperture end where the slope of parabolas is relatively parallel to the optical axis) to reduce the material costs involved with the reflector surface, and change the depth of the collector. Truncation is done at the expense of decrease in maximum concentration ratio while it increases the acceptance angle. The

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Fig. 5. a) Bottom tube sheet and b) Top embossed surface [6].

original acceptance angle (θa) corresponding to the full CPC. In a case when the incident radiation is beyond the original acceptance angle

(θa) and not exceeding the truncated CPC's edge ray angle (θd), all the radiation directly incident on the absorber is accepted while all the radiation intercepted by the reflector is rejected. In this case, the ⎡ ⎤ function Fθ()=1+C ⎢ 1−tan θ ⎥ where C is the new geometric concentra- 2C ⎣ tan θd ⎦ tion ratio after truncation. All the radiation beyond the truncated CPC's

edge ray angle (θd) is rejected and consequently Fθ()=0. In case of cylindrical absorber geometry (refer to Fig. 7), there is a change in the

angular acceptance function between θa and θd which is determined by ⎧ ⎫ ⎡ sin θ ⎤ 1 −⎨ (1 +πC cos θd )⎬ ⎢ ⎩ sin θ ⎭ ⎥ Fθ()=+1 d where C is the new geometric concen- 2 ⎢ 2cosπC θ ⎥ ⎣⎢ ⎦⎥ tration ratio after truncation. The rest of the cases remain same for both flat and cylindrical absorber geometries. A comparison between a truncated CPC with flat absorber and a truncated CPC with cylindrical absorber suggests that the effect of truncation is more prominent in the former with flat absorber. A detailed analysis on the effects of truncation on geometric parameters, optical and thermal performance of CPCs was presented by Rabl [21]. The equations for calculating the truncated aperture fl Fig. 6. Truncated CPC with at absorber [23]. width, height, and the reflector-to-aperture area ratio are mentioned. The method to evaluate average number of reflections inside and outside the original acceptance angle in a truncated CPC is described. The greater the amount of truncation, the lower is the average number of reflections, deviating farther away from the original CPC's average.

3.1.5. Fabrication of CPCs A line-axis CPC with exit aperture width of 0.2 m and acceptance angle of 36° was fabricated using galvanized iron sheets upon which flexible plywood strips glued with mirror material are placed [24]. The whole assembly was encased in an iron channel frame which allowed for inclination adjustments. The absorber used was a black-painted aluminum tube-in-fin type. This CPC accounted for a 76 °C rise in water temperature at no-flow stagnation conditions. Better mirror material and absorber coating would have resulted in further tempera- ture rise. A two-thirds truncated CPC was fabricated using a dark coated mild steel plate as absorber material and a stainless steel sheet as the reflector material [25]. A low iron glass top cover and acrylic side covers were used to prevent convection losses and soiling of the reflector. A tilt mechanism was incorporated to the frame supporting the whole CPC structure allowing tilt adjustments. Fig. 7. Truncated CPC with cylindrical absorber [23]. 3.2. Nonimaging cusp concentrator relationship between the amount of truncation, the concentration ratio and the angular acceptance of radiation is established [23]. An angular Although the cusp concentrator is often referred to as a CPC in the acceptance function – Fθ( ), varying between 0 and 1, was used to literature, the cusp design comprises two distinct curves that are joined determine the amount of radiation accepted by a truncated CPC smoothly. The upper part of the cusp geometry is a parabola while the depending on the angle of incidence (θ) of the radiation. For a lower part (closer to the cylindrical absorber) is a circular or involute truncated CPC with flat absorber geometry (refer to Fig. 6), the shaped geometry. In either case, the curves are smoothly connected to function Fθ()=1and has complete acceptance of radiation below the form the cusp shape. A nonimaging cusp design concentrator was first

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Fig. 8. (a) CPC circular cusp design (b) CPC involute cusp design [27,28]. introduced by Meinel et al. as a patent in 1974 [26]. Winston et al. [27] practical and cost-effective design, truncation of height is necessary. discussed the circular curvature cusp concentrator (as shown in Truncation of the cusp type nonimaging concentrators (of different Fig. 8a) in detail. Rabl [28] analyzed the involute curvature cusp acceptance angles) with cylindrical receivers was discussed by McIntire concentrator (as shown in Fig. 8b). He also derived a differential [32]. The plots of height-to-entrance aperture ratio vs. CR and mirror equation to describe an ideal 2D concentrator with arbitrary convex- arc length-to-entrance aperture ratio vs. CR are useful guidelines in the shaped absorber. As a special case, it was proven that the involute design process of mirror substrates of truncated cusp type concentra- curvature cusp concentrator is the best possible design for cylindrical tors. absorbers. A CPC cusp design (with a cylindrical absorber) as a stationary concentrator was analyzed experimentally, and it was determined that a 32° acceptance angle stationary CPC could collect solar radiation for 6-h daily at a CR of 1.9 all through the year [29]. Truncation decreases the CR to 1.6 while increasing the acceptance angle to 38.7°. The thermal performance of the cusp type CPC collector has been analyzed by Hsieh [30]. The effect of various factors (thermal resis- tance, operating conditions, optical efficiency etc.) on the overall efficiency of the CPC has been discussed. He also recommended that a CPC collector of high concentration ratio should not be installed at geographic locations with high diffuse radiation component owing to the fact that an increased CR lowers the slope as well as the elevation of the CPC efficiency curve. A theoretical numerical model describing the thermal behavior of the CPC cusp type concentrator (with cylindrical absorber) was carried out [31]. The effect of inclination (tilt) when the cusp concentrators are oriented in E-W direction was discussed. The lower the concentration ratio, the more pronounced is the effect of inclination on the CPC collector efficiency. This inverse relationship is attributed to the overwhelming increase in the height and size of the CPC with increasing concentration ratio which in turn suppresses the convective and radiative losses from the absorber and thus, minimizes the effect of inclination. Also, the emphasis of decreasing the convective heat transfer coefficient (hc) in lower inclination CPC collector, which is the dominant contributor to the overall heat transfer coefficient (htot) compared to the radiative (hR) and conductive heat transfer coefficients (hcd), was reiterated.

3.2.1. Truncation of cusp type concentrators Similar to the CPCs, the cusp type concentrators also experience ineffective use of the upper portion of the concentrator. Hence for a Fig. 9. Prism-coupled compound parabolic concentrator [33].

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Fig. 10. Type A concentrator with vertical fin absorber and Type B concentrator with horizontal fin absorber [34].

Fig. 10A and Fig. 10B where dielectric rhombuses are used encapsulat- ing a fin type absorber in vertical and horizontal position respectively [34]. The nonimaging concentrator used in both these designs is a cusp type concentrator with focus of parabolic profile at the intersection of the edge rays (at vertex ‘C’) and center of the circular sector profile at vertex ‘D’. A theoretical analysis suggested that concentration ratios of

2(θa=41.2°, type A) and 1.8 (θa=48.8°, type B) are possible with higher acceptance angles compared to traditional cusp-fin type collectors. Higher acceptance angles along with slightly lower height-to-aperture ratio make them good candidates for stationary applications.

Fig. 11. Near external rays collected by a circular trough of aperture ratio 3.65:1 [36].

3.3. Prism-coupled compound parabolic concentrator

Another nonimaging concentration approach was discussed by Edmonds [33] when he first introduced concept of prism-coupled CPC (PCCPC) to achieve the maximum concentration by a 2D nonimaging concentrator, =( n ) . As shown in Fig. 9, an equilateral sin θ prism is positioned at the exit aperture being the base of the prism. There are two sections to the reflector profile - the ‘BD’ part which a parabola with focus at the apex of the prism –‘F’, and the ‘AB’ part which is a flat line reflector. The angular relationships between the prism apex angle (β), acceptance angle (θ), refractive index (n), angle of the line reflector relative to the axis of symmetry (γ), and angle at which reflected radiation is incident on the prism surface with respect to the axis of symmetry (α) were discussed. The overall conclusion of the theoretical analysis of prism-coupled CPCs show a promising decre- ment in the length-to-aperture ratio for the same amounts of concen- tration yielded by regular CPCs or dielectric CPCs with flat absorbers. Other variations of similar ideas using dielectric material at the absorber level were considered. Two such variations are shown in Fig. 12. Compound elliptical concentrator (CEC) [37].

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3.4. Compound circular arc concentrator (CCAC) collection during a Summer day in Las Vegas, NV [45].

A compound circular arc concentrator (CCAC) is a 2-D non-ideal 3.6.1. Dielectric filled lens-V trough (LVT) concentrator concentrator wherein the parabolic sections of a comparable CPC are The dielectric filled lens-V trough (LVT) concentrator design as replaced by circular sections [35]. 2-D ideal concentrators (CPCs) obey shown in Fig. 13 was experimented with economical dielectric alter- the relationship CR×sin( θmax )=1, whereas this product is less than natives to plastic and glass – water, mineral oil and a combination of unity in the case of 2-D non-ideal concentrators such as CCACs. At low both [39]. A 1.5 mm thick polycarbonate plastic sheet was used to concentration ratios (between 1.5 and 3), the CCACs experienced fabricate the outer casing which was then filled with dielectrics. The energy collection somewhat comparable to analogous CPCs and mineral oil filled LVT (C=2.8) performed better than both the water analogous elliptical concentrators (ECs). However, at higher concen- filled LVT (C=2.4) and combination (water+oil) filled LVT (C=2.8). fl trations, the issue of multiple re ections experienced by CCACs limit When oriented in the E-W direction and tested with a PV absorber, the their optical performance. Nonetheless, CCACs are easier to manufac- power gain factors of 2.35 and 2.07 were obtained. They performed ture using standard sheet metal rollers. well even during overcast conditions suggesting a good acceptance of fi Shapiro also experimented with replacing the parabolic pro le of a diffuse radiation. CPC with a circular arc profile and made an interesting discovery in case of deeper trough CPCs with high concentration ratios [36]. The acceptance half angle of a circular arc profile varied from 12° at the 3.6.2. Dielectric compound parabolic concentrator (DCPCs) center to 21° at the edge of the input aperture as shown in Fig. 11, A dielectric compound parabolic concentrator (DCPC) is a solid fi fi fi whereas, that of a parabolic profile (with same aperture and exit areas CPC con guration. The CPC pro le (2D or 3D) is lled with a dielectric fi of 3.65:1) remained constant at 16° all over the input aperture. Not a material to create a solid CPC con guration. The concept was intro- significant difference is observed in case of shallow trough CPCs with duced mimicking the shape and optical properties of visual receptors in low concentrations and higher acceptance half angles. the compound eye of a horseshoe crab [40]. The DCPCs are character- Multiple reflections affecting the performance of the CCACs diur- ized by their maximum geometric concentration ratio determined by ⎛ ⎞ ⎛ ⎞2 nally as well as through different periods of the year are discussed. A 1/⎜ 1 − 2 ⎟ for 2D-DCPCs and 1/⎜ 1− 2 ⎟ for 3D-DCPCs [41]. The full ⎝ n2 ⎠ ⎝ n2 ⎠ nearly equal performance is reported during hazy weather days and range of angular acceptance θ ∈(0°, 90°) can be achieved by n also near dawn and dusk for both profiles. Sometimes, a circular profile max (refractive index) value ranging from 2 to 2. Such a concentrator is also approximated for a truncated CPC to investigate the compara- would not require any diurnal tracking, just seasonal adjustments. An tive performance. effective increase in the concentration ratio due to the acceptance of non-normal solar irradiance by an E-W oriented DCPC collector is 3.5. Compound elliptical concentrator (CEC) discussed as an additional benefit of DCPCs which makes them an attractive non-tracking concentrator design [42]. However, the issue of The compound elliptical concentrator (CEC) is the design of a Fresnel reflection associated with at the air-dielectric inter- nonimaging concentrator where the parabolic profiles in the CPC face has been neglected. Fresnel reflection lowers the concentration design are replaced by elliptical profiles. In fact, CPC can be proven associated with a DCPC design. as a special case of CEC for an infinite source [37]. The Fig. 12 shows DCPCs (acceptance angle=10.9°, acrylic material (n=1.5)) were the basic geometry of a CEC in which ‘AB’ is the absorber while ‘EF’ is tested with PV cell absorbers and a 3.74 times increase in the peak the radiation source. The elliptical profile - ‘BD’ is part of an ellipse power was observed when compared to a bare cell surface [43]. The whose foci are ‘E’ and ‘A’, and also passing through point ‘B’. Similarly end faces of the CPC are slightly inclined at a 5.5° angle to the vertical. the elliptical profile - ‘AC’ is part of an ellipse whose foci are ‘F’ and ‘B’, This increases the collection of solar radiation when the collector is and also passing through point ‘A’. oriented in E-W direction. The application of 3D CEC reflective element (rotational geometry DCPCs are typically used as secondary concentrators due to the generated by rotation of CEC about the optical axis) as a secondary- dielectric material costs involved. Also, the problem of total internal stage concentrator in a paraboloidal dish concentrator was investigated reflection at the exit aperture-absorber surface interface limited the using raytracing technique [38]. It is concluded that despite the skew- application of DCPCs. This problem was theoretically addressed by ray loss due to CEC, it still has better efficiency compared to a trumpet using the principle of frustrated total internal reflection where the shaped secondary. Furthermore, the compact size of CEC secondary reduces production cost and convective losses while improves its wind resistance.

3.6. Dielectric filled nonimaging concentrators

Using a solid or liquid dielectric fill increases the maximum attainable concentration ratio by a factor ‘n’, where ‘n’ is the refractive index of the dielectric media that is in the path of radiation between the aperture and the absorber. Dielectric solid fill versions of the nonima- ging concentrators need more exploration as they can be potentially strong candidates for stationary applications owing to the fact that they have comparatively higher acceptance angles and, thus, longer diurnal collection of solar energy. However, higher Fresnel reflection losses at the entry aperture for larger incident angles is an issue that needs to be addressed. Applying anti-reflective coatings over the entry aperture can be a partial solution in mitigating this problem. In a simulated analysis, four different dielectric filled nonimaging concentrators namely CPC, CHC, CEC and V-trough were compared with their hollow counterparts as stationary solar concentrators. It is proven that a PMMA dielectric fill would have resulted in a 41–43% increase in diurnal energy Fig. 13. Dielectric filled lens-V trough concentrator [39].

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Fig. 14. a) Trumpet shaped concentrator with extreme rays b) showing complementary external extreme rays reach the external absorber (of width 2c-2a) [50]. absorber is separated by a vacuum gap (less than 200 nm thick) and a asymptote separation angle). The complementary edge-ray string slab of same dielectric material [44]. method was used to prove that trumpet-shaped concentrators, CHC and CEC designs are in fact useful ideal concentrators when applied to 3.7. Dielectric total internally reflecting concentrators (DTIRCs) non-isothermal absorbers and also when preheating by inhomogeneous irradiance of the absorber is preferred [50]. A trumpet shaped The DTIRCs were introduced by Ning et al. [46] and they comprised concentrator is a reflective surface both on the inside as well as the three surfaces – the entry aperture which may be curved, the side walls outside. Notice that the complementary external extreme rays (as (with parabolic, hyperbolic or truncated parabolic profiles) which are shown in Fig. 14b) are aimed at the focus F1 and reached focus F2. All θ causing total internal reflection and an exit aperture. the rays aimed at external absorber at angles greater than a will reach the external absorber as shown in Fig. 14b. 3.8. Dielectric asymmetric compound parabolic concentrators (DiACPCs)

Three different truncated designs of dielectric asymmetric com- pound parabolic concentrators (DiACPCs) with acceptance half angle pairs of (0° and 55°), (0° and 66°) and (0° and 77°) were analyzed using ray-tracing approach for a photovoltaic application at higher northern latitudes ( > 55°N) [47]. The distribution of solar irradiance at the absorber surface is non-uniform for direct radiation and, hence, they recommend the usage of DiACPCs to higher latitudes with larger percentage of diffuse radiation. Mallick et al. [48] fabricated an experimental setup by integration of truncated DiACPC (0° and 50°) with crystalline-Si photovoltaic cells. The comparative experiments showed a promising improvement in the maximum power output over non-concentrating counterparts by 62% for higher latitude geographi- cal region - Belfast in Northern Ireland (54° 36′ N, 5° 37′ W). Another improvement to a similar design of truncated DiACPC (0° and 55°) was proposed [49]. Raytracing and finite element analysis were carried out on the new design where in by adding a reflective film along the bottom edges of the concentrator a 16% increase in the average power output was observed while maintaining cell temperature at 25 °C. However, taking the temperature effects on the PV cell performance into consideration, the increase in the average power output diminished to 6%.

3.9. Compound hyperbolic concentrator (CHC)

Compound hyperbolic concentrator (CHC) is the design of a nonimaging concentrator where the parabolic profiles in the CPC design are replaced by two distinct hyperbolic profiles. A trumpet- shaped concentrator is a special type of CHC.

3.9.1. Trumpet-shaped (flowline) concentrator A trumpet-shaped concentrator has a profile geometry of a single hyperbola as shown in Fig. 14a where F1 and F2 are two foci of the hyperbola profile separated by a distance ‘2c’ with the exit aperture fi being ‘2a’ and the full-acceptance angle being ‘2θa’ (which is also the Fig. 15. Polygonal pro led concentrator [36].

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i) 100% of all the solar radiation is received within the solid angle δ will reach the absorber surface. (provided δπ+∅

The geometric concentration ratio for these types of concentrators is given by: 1 CRv− trough= sin(δ +∅)

Similarly,

dd12− Vertical height of the V−, trough HV− trough = sin ∅

HV− trough 1−sin(δ +∅) Reflector to aperture ratio== R = d1 sin ∅ Previous research has proven that the higher the concentration, the greater is the relative advantage of CPC over the V-trough geometry [11]. At a geometric concentration ratio of 3, the V-trough design seems almost impractical. A quantitative comparison between V-trough Fig. 16. V-trough concentrator with mirror images and reference circle. The rays τδ and and CPC is difficult because of the large number of parameters that τ , have angle of incidence δ and θ , respectively; they pass through the edge of the c c fl absorber and are tangential to the reference circle [11]. should be considered simultaneously. Even disregarding re ector cost and solar energy collection, the comparison involves additional para- meters (R– ratio of reflector to aperture area, <>n - number of reflections, acceptance angle and truncation) besides the value of the concentration ratio. The recent material developments lead to im- proved reflective surfaces which may improve the overall year round efficiency of a nonimaging CPCs with polygonal or V-type profile compared to parabolic profile in low and medium concentration applications.

3.11. Tailored edge-ray concentrators (TERCs)

A further developed extension of the edge-ray principle (also known as simultaneous multiple surface design method) led to the design of the group of concentrators known as the TERCs. They have at least two Fig. 17. Angular acceptance of V-trough varying with the angle of incidence [11]. optically interactive surfaces. These concentrators are named after the optical interactions involved in the transfer of from input fi 3.10. Polygonal and V-trough pro le geometry aperture to exit aperture (R stands for refractive, and X stands for reflective). Viz. an RR concentrator has both refractive surfaces, XR fi A polygonal pro le (as shown in Fig. 15) instead of a parabolic concentrator has a reflective surface, and a refractive surface. All the fi pro le for a CPC was investigated theoretically [36]. An aperture ratio three designs – XR, RR and RX – are discussed in detail by Miñano (inlet-to-exit) of 8:1 was used. Two plane mirrors made out of polished et al. [51,52] and are as shown in Fig. 18. The XR concentrator is an metal sheet are bent symmetrically at two equidistant points. The assembly of two pieces – areflecting element and a refracting element. upper segment, the middle segment and the lower segment make 3°, 6° The RR concentrator is an aspheric lens. The RX concentrator is a and 9° bends with respect to the axial plane of the concentrator single piece comprising both refracting and reflecting interfaces. The fi respectively as shown in the gure below. The acceptance half angle of RX concentrator requires much more dielectric material than a ′ this concentrator also varied from 7° at the center to 11°30 at the comparative XR concentrator and, hence, more suitable in the scenario extremity of the aperture compared to a constant acceptance half angle where the cost of dielectric material is not critical. In general, all these ′ fi throughout of 7°11 for a CPC with parabolic pro le. This additional designs perform well under etendue with smaller angular spread i.e. advantage results in the collection of greater amount of radiation at an lower acceptance angles. The acceptance angles of these concentrators fl fl expense of multiple re ections (up to a maximum of 5 re ections). are generally constrained to less than 10°, this makes them potential fi Hence, the performance of such pro le geometry is highly dependent candidates for coupling with passive tracking mechanism. on the reflectance of the mirror material. The V-trough concentrator geometry is as shown in Fig. 16. The 3.12. Nonimaging Fresnel lenses non-hatched surface forms the reflector surface of the V-trough concentrator. Two angles – Φ (half angle of the v-shaped cone) and δ Nonimaging optical sciences were applied to Fresnel lenses and (complete acceptance angle) – play an important role in determining began to be widely used in the field of solar concentration. Fresnel the amount of energy collected by a V-shaped geometry. One of the lenses of nonimaging design are usually of convex shape in order to get following 3 scenarios determines the complete or partial acceptance of high concentration ratios and flux distributions with short focal length. the solar radiation by a V-trough concentrator (as shown graphically on The main characteristic of the nonimaging systems is their concentra- Fig. 17). tion ratios (i.e. the geometric concentration ratio C) which are

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Fig. 18. Tailored edge-ray concentrators (also known as SMS concentrators) – RR, XR and RX designs [8,51,52]. commonly classified as being low for C≤10, or medium for 10 < C≤100, 3.13. Two-stage or multi-stage nonimaging concentrator or high for C > 100. The use of linear convex Fresnel lenses (with acceptance angles 30°, Various nonimaging concentrators such as the CPC, CEC, hyper- 40° and 50°) was investigated using a ray-tracing approach in both E- bolic trumpet shaped concentrator etc. are actively considered as W and polar orientations [53]. As expected, the focal points were closer secondary or tertiary optical elements to increase the geometric together as the acceptance angle decreased which results in a higher concentration ratio and/or to fold (decrease) the optical path length temporary concentration. Also, the diurnal movement of the Sun [55]. They are particularly useful if higher absorber temperatures are caused focal length shortening. The greater the solar azimuth angle, desired and if the primary optical elements (e.g. paraboloidal dish) are the shorter is the focal length. Receiver tracking was considered an susceptible to concentration errors. A nonimaging receiver was pro- alternative to overcome this setback. Another alternative approach is to posed for parabolic trough concentrating collectors where an increased elliptically assemble a series of receivers along the focal path and allow overall (thermal+optical) efficiency of 1.4% was observed [56]. the interaction of working fluid only with those absorbers that are Although their absorber design was not cost-effective, it provided active by using thermostatically controlled valves. improved flux uniformity and increased tolerance towards concentra- Linear convex Fresnel lens systems were designed to achieve 10X tion errors. concentration (primary-5X+secondary-2X) with the means of second- Two-stage PV concentrators with a point-focusing Fresnel lens as ary CPC or other non-imaging concentrator [54]. The secondary the primary stage and a dielectric total internally reflecting concen- concentrator also homogenizes the Gaussian distribution of the trator (DTIRC) as the secondary stage were discussed by Ning et al. Fresnel lens concentrated radiation resulting in more homogeneous [57]. Both the ray-tracing and the experimental results showed that the illumination conditions for PV applications. Light is scattered due to two-stage concentrator offered better acceptance angle and higher total internal reflection from the facet walls of the individual prismatic concentration compared to the point-focusing Fresnel lens alone. elements of a Fresnel lens and is known as the shadowing effect. This Additionally, it also provided a more uniform flux distribution that causes a loss in the incident radiation which is related to the maximum improved the PV cell performance. deflection angle of the lens Viz. a maximum deviation of 10.5° reduces Multistage collection of solar radiation was attempted by Collares- the mean annual performance by 7%. Pereira et al. in 1977 [58]. The collector arrangement is a primary

11 S. Madala, R.F. Boehm Renewable and Sustainable Energy Reviews (xxxx) xxxx–xxxx convex lens and the secondary mirror arrangement. A hyperbolic COP of 0.19. These systems provided chilled water at 15 °C from shaped mirror is used instead of an elliptic shape to achieve better 11 A.M. to 3:30 P.M. The thermal efficiency of the CPC collectors were concentration. In order to facilitate fabrication, the shape of the comparatively higher than traditional collector at higher operating fluid hyperbola can be modified to a V-shaped profile without substantial (water) temperatures. losses.

4. Recent developments in nonimaging solar optics 4.2. Optical modeling using computer programs

Coincidentally, CPC design is a biomimicry of the ommatidium in The field of optical modeling has seen tremendous progress in the the compound eye of a horse-shoe crab that evolved millions of years past two decades due to the exponential increase in computing power. ago. Since the invention and application of the earliest nonimaging Early optical modeling efforts on CPCs involved using multiple concentrator – CPC to collect solar energy, various nonimaging programs to achieve the desired ray-tracing results. Viz. AutoCAD collectors have seen diverse applications as solar energy collectors. was used in conjunction with LOTUS 1–2–3 and FORTRAN to model Solar-pumped lasers are setup using nonimaging Fresnel lenses [59]. and ray-trace a cusp-type CPC with cylindrical absorber [64]. Other applications involve concentrated photovoltaics, solar thermo- Currently, there are commercially available optical modeling soft- photovoltaic systems etc. ware that can be handy in optical modeling of various designs. These programs can be broadly classified into 3 categories: sequential ray- 4.1. Fields of application tracing type, non-sequential ray-tracing type and finite-difference time- domain (FDTD) simulation type. Sequential ray-tracing software Demonstration of building integrated photovoltaics with a station- interacts with the light from a user-defined source in a sequentially ary arrangement of nonimaging concentrators was conducted using defined manner. Each surface in the optical system interacts with the two different concentrator designs – a linear convex Fresnel lens (10X light one at a time in the order defined by the user. These type of concentration) and a combination of linear convex Fresnel lens (5X programs are typically used to model optical systems such as cameras, concentration) with CPC (2X concentration) [54]. endoscopes, microscopes, telescopes etc. Examples of such programs Buildings in non-seismic, snow accumulation regions (typically are CODE V, ASAP etc. On the other hand, non-sequential programs higher latitude regions) are most suitable for installing a mid- allow the ray interaction with any surface multiple times without any temperature range (80–250 °C) stationary nonimaging solar collector predetermined sequence. Ray-scattering and Fresnel reflections are [60]. Four different nonimaging collector configurations – CPC, sea effectively accounted for, leading to more accurate modeling of real shell with upper reflector, sea shell with adjustable reflector and world interactions. Some non-sequential optical modeling programs vertical asymmetric CPC – coupled with evacuated tubes were con- can also model coherent systems through the Gaussian beam summa- sidered as a part of a case study for building integration. The suitable tion method. These type of programs are typically used to model building types, structural and reflector details were discussed. imaging systems, light pipes, backlights, luminaires etc. Examples of Solar photocatalytic detoxification of water is the removal of such programs are Optics Lab, ZEMAX, OSLO, TracePro, FRED, Light hazardous and non-biodegradable wastes using the near-ultraviolet Tools etc. When the size of the optical system shrinks to the band of the solar spectrum (wavelength under 390 nm). The UV wavelength-scale, the Gaussian beam summation modeling breaks radiation photoexcites a semiconductor catalyst (typically TiO2)to down. That is when FDTD programs come in handy. They solve for promote oxidative and reductive reactions. Under the SOLARDETOX Maxwell's equations to propagate electro-magnetic fields through project, a detoxification plant was built that incorporated two rows of micro and nano-scale optical systems. Examples of such programs 21 modules of cusp type CPC collectors (oriented in E-W direction) are Virtual Lab, SPEOS etc [65]. with a total aperture area of 100 m2 and a loop capacity of 800 l/cycle Optical simulation software such as TracePro, OptiCAD and ASAP [61]. had been reportedly used to simulate the performance of nonimaging Prospective application of the nonimaging optics in laser fiber optic Fresnel lens or nonimaging optics in general [44,66]. Optimization surgical procedures was discussed [62]. The increase in irradiance with algorithms are frequently embedded in these types of software to maximum collection efficiency and uniform distribution over a wider perform design optimization of a newer design. OptiCAD was used to angular range are the motivating factors when compared to imaging compare the optical performance of a linear Fresnel lens (10X optics or tapered V-cone type devices. concentration), and a hybrid system of linear Fresnel (5X

A lithium bromide-water (LiBr-H2O) based solar absorption cool- concentration)+CPC (2X concentration) [37]. This 3D analysis showed ing system was coupled with CPC solar collectors with evacuated tube the effect of transverse and longitudinal angles on focus and the optical receivers and tested in Jinan City, China (36.65°N, 117.12°E) [63]. The concentration ratio. The hybrid system of 5X linear Fresnel lens +2X CPC solar collectors (105 m2) that were oriented in N-S direction at a CPC proved more effective for stationary applications (BIPV in this tilt angle of 20° achieved an average cooling capacity of 9.2 kW at a case).

Passive Solar Tracking Systems

Thermohydraulic actuator Bimetallic thermal actuator Shape memory alloy thermal mechanism. mechanism. actuator mechanism. E.g. Refrigerant (phase- E.g. Al and Steel bimetallic E.g.CuZnAl and CuAlNi change fluid) thermal strip etc. based shape memory alloys expansion

Fig. 19. Classification of passive tracking systems.

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profile concentrator, TERCs, nonimaging Fresnel lens, two-stage and multi-stage nonimaging concentrators. Most of these concentrator designs perform well as stationary or passive tracking concentrators for low to medium concentration ratios (1-3X and 3-10X). Multi-stage concentrators show the versatile usefulness of nonimaging concentra- tors not only in achieving higher concentration but also in achieving it economically. However, care must be taken not to go lower than 3° acceptance angle while designing a passive tracking nonimaging concentrator as it affects circumsolar radiation collection, an important design criteria to consider when coupling with passive tracking systems. Dielectric solid fill versions of the nonimaging concentrators are potentially strong candidates for stationary applications as they have comparatively higher acceptance angles and, thus, longer diurnal collection of solar energy. However, higher Fresnel reflection losses at the entry aperture for larger incident angles is an issue that needs to be addressed more effectively as anti-reflective coatings can only be partial Fig. 20. Permissible single-axis tracking error vs. the concentration ratio for a hollow CPC design. solutions. This paper also discusses various novel applications of nonimaging collectors from integration in BiPVs to the solar photo- fi 5. Passive-tracking nonimaging systems catalytic detoxi cation of water. Finally, some of the recent develop- ments in ray-tracing algorithms that help in optical modeling of As the focus of this paper is on stationary and passive nonimaging nonimaging concentrators, and passive tracking technologies that can concentration systems, it is only relevant to include some discussion on be potentially coupled with nonimaging concentrators are also dis- advancements in passive solar tracking systems. They are a particularly cussed. attractive option owing to their simplistic, low-cost design. As opposed to the active solar tracking mechanism which uses certain portion of References the auxiliary power (electrical power) to drive it's tracking mechanism, the passive tracking mechanism is driven by changing physical [1] Janet L. Sawin, Kristin Seyboth, Freyr Sverrisson FA, Adam Brown, Bärbel Epp, Anna Leidreiter, Christine Lins, Hannah E. Murdock, et al. Renewables 2016 global attributes due to the diurnal motion of the sun. status report. Paris; 2016. [doi: ISBN 978-3-9818107-0-7]. Passive tracking systems are based on differential thermal expan- [2] NREL-SolarPACES. NREL: Concentrating solar power projects – concentrating 〈 sion of materials such as refrigerants, bimetallic strips or shape solar power projects by project name. Webpage 2016. http://www.nrel.gov/csp/ solarpaces/by_project.cfm〉 [accessed 24.10.16]. memory alloys. 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